MATLAB Implementation of Particle Filter Algorithm with Residual Resampling Technique

In this article, we explore the implementation of the particle filter algorithm, which incorporates a specialized resampling technique known as residual resampling. The primary objective of this algorithm is to achieve accurate target tracking by systematically adjusting particle weights. Residual resampling, a Monte Carlo-based sampling approach, preserves a predetermined number of particles during the resampling phase, effectively reducing sampling errors and enhancing tracking performance. The implementation typically involves initializing particles with random states, propagating them through system dynamics using prediction models, calculating importance weights based on measurement likelihoods, and executing residual resampling when effective sample size falls below a threshold. This resampling method deterministically retains particles with high weights while stochastically redistributing the remaining ones. Beyond particle filters, numerous tracking alternatives exist, including Extended Kalman Filters (EKF) and Unscented Kalman Filters (UKF). However, particle filters demonstrate superior adaptability and flexibility compared to other tracking techniques, primarily due to their capability to handle nonlinear systems and non-Gaussian distributions without linearization approximations. The MATLAB implementation typically utilizes functions like randn for noise generation, system equations for state propagation, and custom residual resampling loops for weight normalization and particle selection.